7.1 Integration By Parts/53: Difference between revisions
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| Line 5: | Line 5: | ||
\begin{align} | \begin{align} | ||
\underbrace{\int_{0}^{5}xe^{-0.4x}dx} | \underbrace{\int_{0}^{5}xe^{-0.4x}dx}_{ | ||
\begin{aligned} | \begin{aligned} | ||
| Line 12: | Line 12: | ||
u &= x & dv &= e^{-0.4x} dx \\[0.6ex] | u &= x & dv &= e^{-0.4x} dx \\[0.6ex] | ||
du &= dx & v &= \frac{5}{2}e^{-0.4x} | du &= dx & v &= \frac{5}{2}e^{-0.4x} | ||
\end{aligned} \\ [2ex] | \end{aligned}} \\ [2ex] | ||
\end{align} | \end{align} | ||
Revision as of 12:53, 13 December 2022
![{\displaystyle {\begin{aligned}\underbrace {\int _{0}^{5}xe^{-0.4x}dx} _{\begin{aligned}u&=x&dv&=e^{-0.4x}dx\\[0.6ex]du&=dx&v&={\frac {5}{2}}e^{-0.4x}\end{aligned}}\\[2ex]\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/91d4a6c6285a2e1341ff3df89604c6777da55fd6)
![{\displaystyle \left[{\frac {5}{2}}e^{-0.4x}\right]+\int _{5}^{0}{\frac {5}{2}}e^{-0.4x}dx}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/4afefe06edf9bd3affd7c306ac9be17807450731)